Question

Balance the following reaction by oxidation number method: $As_{2}S_{5}+H^{+}NO_{3}^{-}(conc.) \longrightarrow H_{3}AsO_{4}+5H_{2}SO_{4}+H_{2}O+NO_{2}$

Answer 1

Basic skeleton of the reaction

${ As }_{ 2 }{ S }_{ 5(s) }\quad +\quad { HNO }_{ 3(aq) }\quad \rightarrow \quad { H }_{ 3 }As{ O }_{ 4(aq) }\quad +\quad { H }_{ 2 }{ SO }_{ 4(aq) }\quad +\quad { NO }_{ 2(g) }$

Assign oxidation numbers for the reaction

${ As }_{ 2 }^{ +5 }{ S }_{ 5 }^{ -2 }\quad +\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad \rightarrow \quad { H }_{ 3 }^{ +1 }{ As }^{ +5 }{ O }_{ 4 }^{ -2 }\quad +\quad { H }_{ 2 }^{ +1 }{ S }^{ +6 }{ O }_{ 4 }^{ -2 }\quad +\quad { N }^{ +4 }{ O }_{ 2 }^{ -2 }$

Identify the redox couples

$O:\quad { As }_{ 2 }^{ +5 }{ S }_{ 5 }^{ -2 }\quad \rightarrow \quad 5{ H }_{ 2 }^{ +1 }{ S }^{ +6 }{ O }_{ 4 }^{ -2 }\quad +\quad 40{ e }^{ - }$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad { e }^{ - }\quad \rightarrow \quad { N }^{ +4 }{ O }_{ 2 }^{ -2 }$

Combine the redox couples.

$O:\quad { As }_{ 2 }^{ +5 }{ S }_{ 5 }^{ -2 }\quad \rightarrow \quad 5{ H }_{ 2 }^{ +1 }{ S }^{ +6 }{ O }_{ 4 }^{ -2 }\quad +\quad 40{ e }^{ - }$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad { e }^{ - }\quad \rightarrow \quad { N }^{ +4 }{ O }_{ 2 }^{ -2 }$

Balance all the atoms expect oxygen and hydrogen

$O:\quad { As }_{ 2 }^{ +5 }{ S }_{ 5 }^{ -2 }\quad \rightarrow \quad 5{ H }_{ 2 }^{ +1 }{ S }^{ +6 }{ O }_{ 4 }^{ -2 }\quad +\quad 2{ H }_{ 3 }As{ O }_{ 4 }\quad + \quad 40{ e }^{ - }$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad { e }^{ - }\quad \rightarrow \quad { N }^{ +4 }{ O }_{ 2 }^{ -2 }$

Balance the charge.

$O:\quad { As }_{ 2 }^{ +5 }{ S }_{ 5 }^{ -2 }\quad \rightarrow \quad 5{ H }_{ 2 }^{ +1 }{ S }^{ +6 }{ O }_{ 4 }^{ -2 }\quad +\quad 2{ H }_{ 3 }As{ O }_{ 4 }\quad + \quad 40{ e }^{ - }\quad + \quad 40{ H }^{ + }$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad { e }^{ - }\quad +\quad { H }^{ + }\quad \rightarrow \quad { N }^{ +4 }{ O }_{ 2 }^{ -2 }$

Balance oxygen atoms.

$O:\quad { As }_{ 2 }^{ +5 }{ S }_{ 5 }^{ -2 }\quad +\quad 28{ H }_{ 2 }O\quad \rightarrow \quad 5{ H }_{ 2 }^{ +1 }S\quad +\quad 6{ O }_{ 4 }^{ -2 }\quad +\quad 2{ H }_{ 3 }As{ O }_{ 4 }\quad +\quad 40{ e }^{ - }\quad +\quad 40{ H }^{ + }$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad { e }^{ - }\quad +\quad { H }^{ + }\quad \rightarrow \quad { N }^{ +4 }{ O }_{ 2 }^{ -2 }\quad +\quad { H }_{ 2 }O$

$O:\quad { As }_{ 2 }^{ +5 }{ S }_{ 5 }^{ -2 }\quad +\quad 28{ H }_{ 2 }O\quad \rightarrow \quad 5{ H }_{ 2 }^{ +1 }{ S }^{ +6 }{ O }_{ 4 }^{ -2 }\quad +\quad 2{ H }_{ 3 }As{ O }_{ 4 }\quad +\quad 40{ e }^{ - }\quad +\quad 40{ H }^{ + }$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad { e }^{ - }\quad +\quad { H }^{ + }\quad \rightarrow \quad { N }^{ +4 }{ O }_{ 2 }^{ -2 }\quad +\quad { H }_{ 2 }O$

Make electron gain equivalent to electron lost

$O:\quad { As }_{ 2 }^{ +5 }{ S }_{ 5 }^{ -2 }\quad +\quad 28{ H }_{ 2 }O\quad \rightarrow \quad 5{ H }_{ 2 }^{ +1 }S\quad +\quad 6{ O }_{ 4 }^{ -2 }\quad +\quad 2{ H }_{ 3 }As{ O }_{ 4 }\quad +\quad 40{ e }^{ - }\quad +\quad 40{ H }^{ + }$

$R:\quad { H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad { e }^{ - }\quad +\quad { H }^{ + }\quad \rightarrow \quad { N }^{ +4 }{ O }_{ 2 }^{ -2 }\quad +\quad { H }_{ 2 }O$

$O:\quad { As }_{ 2 }^{ +5 }{ S }_{ 5 }^{ -2 }\quad +\quad 28{ H }_{ 2 }O\quad \rightarrow \quad 5{ H }_{ 2 }^{ +1 }S\quad +\quad 6{ O }_{ 4 }^{ -2 }\quad +\quad 2{ H }_{ 3 }As{ O }_{ 4 }\quad +\quad 40{ e }^{ - }\quad +\quad 40{ H }^{ + }$

$R:\quad 40{ H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ -2 }\quad +\quad 40{ e }^{ - }\quad +\quad 40{ H }^{ + }\quad \rightarrow \quad 40{ N }^{ +4 }{ O }_{ 2 }^{ -2 }\quad +\quad 40{ H }_{ 2 }O$

Add the half reactions together

${ As }_{ 2 }^{ +5 }{ S }_{ 5 }^{ -2 }\quad +\quad 40{ H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ +2 }\quad +\quad 28{ H }_{ 2 }O\quad +\quad 40{ e }^{ - }\quad +\quad 40{ H }^{ + }\quad \rightarrow \quad 5{ H }_{ 2 }^{ +1 }{ S }^{ +6 }{ O }_{ 4 }^{ -2 }\quad +\quad 40{ N }^{ +4 }{ O }_{ 2 }^{ -2 }\quad +\quad 2{ H }_{ 3 }As{ O }_{ 4 }\quad +\quad 40{ H }_{ 2 }O\quad +\quad 40{ e }^{ - }\quad +\quad 40{ H }^{ + }$

Simplify the equation

${ As }_{ 2 }^{ +5 }{ S }_{ 5 }^{ -2 }\quad +\quad 40{ H }^{ +1 }{ N }^{ +5 }{ O }_{ 3 }^{ +2 }\quad \rightarrow \quad 5{ H }_{ 2 }^{ +1 }{ S }^{ +6 }{ O }_{ 4 }^{ -2 }\quad +\quad 40{ N }^{ +4 }{ O }_{ 2 }^{ -2 }\quad +\quad 2{ H }_{ 3 }As{ O }_{ 4 }\quad +\quad 12{ H }_{ 2 }O$

Final equation is  

${ As }_{ 2 }{ S }_{ 5 }\quad +\quad 40{ HNO }_{ 3 }\quad \rightarrow \quad 2{ H }_{ 3 }As{ O }_{ 4 }\quad +\quad 5{ H }_{ 2 }{ SO }_{ 4 }\quad +\quad 40{ NO }_{ 2 }\quad +\quad 12{ H }_{ 2 }O$